1.1 Field of the Invention
This invention relates to the field of well logging and, more particularly, to improved methods for processing electromagnetic (EM) measurements acquired with a logging tool disposed within homogeneous anisotropic formations to determine parameters of the formation.
1.2 Description of Related Art
Induction logging is a well-known form of EM logging in the field of hydrocarbon exploration and production. Conventional induction logging tools include a transmitter and a receiver array consisting of a set of coil antennas mounted on a support and axially spaced from each other in the direction of the borehole. The transmitter antenna is energized by an alternating current, which in turn generates an electric field that induces eddy currents in the formation surrounding the borehole. The intensity of the eddy currents is proportional to the conductivity of the formation. The field generated in turn by these eddy currents induces an electromotive force in the receiver antenna. The signals detected at a receiver antenna are usually expressed as a complex number (phasor voltage) and reflect interaction with the borehole fluid and the formation. By processing the acquired measurements, the formation and/or borehole parameters are determined.
A coil carrying a current can be represented as a magnetic dipole having a magnetic moment proportional to the current and the area encompassed by the coil. The direction and strength of the magnetic dipole moment can be represented by a vector perpendicular to the area encompassed by the coil. Typical logging tools are equipped with coils of the cylindrical solenoid type comprised of one or more turns of insulated conductor wire. Some logging tools are also implemented with saddle coil or flex circuit antenna configurations.
In conventional induction and propagation logging tools, the transmitter and receiver antennas are generally mounted with their axes along the longitudinal axis of the tool. An emerging technique in the field of well logging is the use of logging tools incorporating antennas having tilted or transverse coils, i.e., where the coil""s axis is not parallel to the longitudinal axis of the support. These tools are thus implemented with antennas having a transverse or tilted magnetic dipole. One particular implementation uses a set of three coils having non-parallel axes (referred to herein as tri-axial). FIG. 1 shows a tri-axial transmitter and receiver antenna system wherein the coil axes are independently directed. The aim of these antenna configurations is to provide three-dimensional formation evaluation, including information about resistivity anisotropy in vertical wells and directional sensitivity to bed boundaries that can be used for navigation. Logging tools equipped with tri-axial antenna systems are described in U.S. Pat. Nos. 5,115,198, 5,781,436, 6,147,496, 5,757,191 and WO 00/50926.
The techniques for processing the acquired EM measurements into representative values of the formation parameters involve a number of mathematical calculations. U.S. Pat. No. 4,302,722 (assigned to the present assignee) describes techniques for determining formation conductivity and anisotropy parameters from the acquired measurements. U.S. Pat. Nos. 5,781,436, 5,999,883 and 6,044,325 describe methods for producing estimates of various formation parameters from tri-axial measurements.
It is desirable to obtain a simplified technique for processing EM measurement data, acquired from a logging tool, to determine parameters of a subsurface formation. Thus, there remains a need for simplified techniques for calculating complete couplings of tri-axial measurements to determine the formation parameters.
Systems and methods are provided for determining various subsurface formation parameters from electromagnetic measurements. The measurements are acquired with a logging tool adapted with a system of tri-axial transmitter and receiver antennas disposed within the formation.
One aspect of the invention provides a method for determining a formation parameter from EM measurements acquired with a tri-axial system of antennas. The method includes determining antenna couplings associated with the measurements. The following expression is then derived from the couplings and calculated to determine the horizontal conductivity of the formation:
xe2x80x83(Txe2x80x2zzxe2x88x92Lh)(Txe2x80x2xxxe2x88x92Th)=(Txe2x80x2xz)2,
where Txe2x80x2zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna; Txe2x80x2xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna; Txe2x80x2xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna; and Lh, Th are elementary functions corresponding to the couplings of said antennas.
Another aspect of the invention provides a method for determining a formation parameter from EM measurements acquired with a tri-axial system of antennas. The method includes determining antenna couplings associated with the measurements. The following expression is then derived from the couplings and calculated to determine the horizontal conductivity "sgr"h of the formation:             σ      h        =                            8          ⁢          π          ⁢                      xe2x80x83                    ⁢          r                ωμ            ⁢                                    Im            ⁢                          {                              T                xx                xe2x80x2                            }                        ⁢            Im            ⁢                          {                              T                zz                xe2x80x2                            }                                -                      Im            ⁢                                          {                                  T                  xz                  xe2x80x2                                }                            2                                                            2            ⁢                          xe2x80x83                        ⁢            Im            ⁢                          {                              T                xx                xe2x80x2                            }                                -                      Im            ⁢                          {                              T                zz                xe2x80x2                            }                                            ,
where Txe2x80x2xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna; Txe2x80x2zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna; Txe2x80x2xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna; xcfx89 represents an angular frequency; r is a separation distance between the antennas; and xcexc is a magnetic permeability constant.
Another aspect of the invention provides a system for determining a formation parameter from electromagnetic measurements. The system includes a tool adapted for disposal within the formation and equipped with a tri-axial system of transmitter and receiver antennas. The system further includes computation means for determining antenna couplings associated with the measurements, and for calculating the following expression derived from the couplings to determine the horizontal conductivity of the formation:
(Txe2x80x2zzxe2x88x92Lh)(Txe2x80x2xxxe2x88x92Th)=(Txe2x80x2xz)2,
where Txe2x80x2zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna; Txe2x80x2xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna; Txe2x80x2xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna; and Lh, Th are elementary functions corresponding to the couplings.
Another aspect of the invention provides a system for determining a formation parameter from electromagnetic measurements. The system includes a tool adapted for disposal within the formation and equipped with a tri-axial system of transmitter and receiver antennas. The system further including computation means for determining antenna couplings associated with the measurements, and for calculating the following expression derived from the couplings to determine the horizontal conductivity "sgr"h of the formation:             σ      h        =                            8          ⁢          π          ⁢                      xe2x80x83                    ⁢          r                ωμ            ⁢                                    Im            ⁢                          {                              T                xx                xe2x80x2                            }                        ⁢            Im            ⁢                          {                              T                zz                xe2x80x2                            }                                -                      Im            ⁢                                          {                                  T                  xz                  xe2x80x2                                }                            2                                                            2            ⁢                          xe2x80x83                        ⁢            Im            ⁢                          {                              T                xx                xe2x80x2                            }                                -                      Im            ⁢                          {                              T                zz                xe2x80x2                            }                                            ,
where Txe2x80x2xx is the coupling between an x-axis receiver antenna and an x-axis transmitter antenna; Txe2x80x2zz is the coupling between a z-axis receiver antenna and a z-axis transmitter antenna; Txe2x80x2xz is the coupling between an x-axis receiver antenna and a z-axis transmitter antenna; xcfx89 represents an angular frequency; r is a separation distance between the antennas; and xcexc is a magnetic permeability constant.